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THE ORGANIZATION OF THE ROSETTA GRAMMARS
Jan Odijk
Philips Research Laboratories, P.O. Box 80.000
5600 JA Eindhoven, The Netherlands
ABSTRACT
In this paper the organization of the gram-
mars in the Rosetta machine translation system
is described and it is shown how this organization
makes it possible to translate between words of dif-
ferent syntactic categories in a systematic way. It
is also shown how the organization chosen makes it
possible to translate 'small clauses' into full clauses
and vice versa. The central concept worked out
here in some detail is the concept of 'partial iso-
morphy' between subgrammars. The system as de-
scribed here has been implemented and is currently
being tested.
1 ROSETTA
In this section I will mention some essential prop-
erties of the Rosetta machine translation system.
For more extensive descriptions of this system I
refer to Landsbergen(1987), Appelo & Landsber-
gen(1986), Appelo, Fellinger & Landsbergen(1987)
and Leermakers & Rous(1986).
The Rosetta machine translation system is an
interlingual machine translation system based on
Montague Grammar and developed at Philips Re-
search Laboratories in Eindhoven for Dutch, En-
glish and Spanish. The grammars used in Rosetta
are computational variants of Montague Grammar
and are called M-grammars.

Rules in M-grammars, called M-rules, operate
on syntactic surface trees. If a certain string
str
is
associated with a syntactic tree of category C the
notation
C(str)
will be used.
An M-grammar in Rosetta is subdivided into a
number of subgrammars. Each subgrammar is a
rule package and is defined by specifying a
head
(the category of a designated argument from the
import for the subgrammar),
export
(the categories
of the syntactic trees yielded by the subgrammar)
and a
control expression
that indicates in which
order M-rules must be applied.
In Rosetta31 a distinction is made between
meaningful M-rules, called
rules
(that correspond
to a meaning operation), and meaningless rules,
called
transformations
(that do not correspond to
a meaning operation).

M-grammars are reversible. Because of this fact,
the translation relation between two sentences can
be illustrated by showing their derivations ill gen-
eration. The example derivations below will be
restricted to generation only.
Within the Rosetta system the grammars of the
relevant languages are attuned to one another,
in such a way that two sentences that are each
other's translation can be derived starting from
corresponding basic expressions by applying COlTe-
sponding rules in the same way for both sentences.
'Corresponding' here means: 'corresponding to the
same meaning operation or basic meaning', and it
holds of meaningful M-rules only.
M-grammars attuned in this way are called
iso-
morphic grammars,
and therefore the method of
translation used is called the
isomorphic grammar
approach to machine translation.
2
CATEGORIAL
MISMATCHES
In order to derive simple sentences e.g.
Ziet hi 3" de
manf
one could design a grammar of Dutch that,
starting with a basic verb
(zie)

applies rules to de-
rive the sentence mentioned. One could have rules
combining a basic verb with arguments that it al-
lows or requires
(hij, de mart)
in a sentence, rules
that determine the tense of this sentence
(present
tense)
and rules that determine 'mood' and real-
ÂThe.pap-er-d-ea~-with the grammars in the third version
of the Rosetta system, Rosetta3.
- 80 -
ize the sentence accordingly ( in this case yes-no-
question, main clause, realized by the order verb-
subject-object}, etc
In order to derive the English sentence
Does he
see the
manf
as a translation of this Dutch sen-
tence it would be required to design a grammar
of English isomorphic to the grammar of Dutch
sketched above. There must be a rule combining a
verb (see} with its arguments (he,
the man}.
There
must be rules determining tense and aspect
(simple
present tense

in the example sentence), and there
must be rules that determine 'mood' and realize
the sentence accordingly (yes-no- question, main
clause, realized by introducing the auxiliary verb
do
and the order do-subject-verb-object}, etc
In this simple example the syntactic categories of
the
Dutch word
zien
and its translation into En-
glish
see are
the same. For these cases isomor-
phic grammars can be developed rather straight-
forwardly.
However, machine translation systems must be
able not only to translate between words of the
same category, but also to translate between words
of different syntactic categories. Some examples
where a translation between words of different cat-
egories is required or desirable are given in the fol-
lowing table:
hij zwemt graag (Adv}
he likes to swim (Verb}
hij is toevallig ziek (Adv)
he happens to be ill (Verb}
het mist (Verb}
it is foggy (Adj)
hij schaamt zich ervoor (Verb}

He (_Adj.!

hij is mij 3 gulden schuldig (Adj)
He owes me 3 guilders (Verb}
hij is in A'dam woonaehtig (Adj)
He resides in Amsterdam (Verb}
Het is voldoende (Adj}
The Rosetta grammars nmst be able to deal with
such cases in a systematic way.
It must also be possible to translate 'small
clauses' into full clauses (finite or infinite) and vice
versa. 'Small Clauses' are propositional units in
which a subject-predicate relationship is expressed
and which are not marked for tense and aspect (cf.
Stowell (1981)). Some examples of full clauses and
their corresponding 'small clauses' are given in the
following table:
'Full Clauses'
Verb
Adj
Prep
Adv
Noun
He killed a man
He is intelligent
He is against the deal
He is here
He is a fool
'Small Clauses'
Verb

Adj
Prep
Adv
Noun
I had the man killed
I consider him intelligent
We got him against the deal
We got him here
They consider him a fool
Small clauses can occur only as complements
within a clause. The fact that they are not marked
for tense and aspect is reflected in the absence of
auxiliary and copular verbs. If the grammar al-
lows for translation of clauses into small clauses
and vice-versa, then it becomes possible to derive
e.g. he seems ill and hii schiint ziek te zijn (lit.
he seems to be ill as translations of each other. It
is sometimes requh'ed to be able to translate small
clauses into full clauses in some cases. The En-
glish sentence he seems ill cannot be translated
into Dutch *hi i schiint ziek, which is ungrammat-
ical, but umst be translated into hi] schi]nt ziek te
zijn ( he seems to be ill) or into bet schiint dat hi i
ziek is (it seems that he is ill}.
3
GRAMMAR ORGANI-
ZATION
The global organization of the grammars (leaving
transformations out of consideration) is the same
for all languages, as is required by the isomorphic

method.
The grammars are subdivided into five proiec-
tion subgrammars ~, one for each major category
(Verb, Noun, Prep, Adj, Adv). 3
Each of these projection subgrammars consists
of a number of subgrammars. The partitioning of
projection subgrammars into subgrammars is mo-
tivated by the fact that it must be possible to use
tile output of each subgrammar as import to sub-
grammars of other projection subgrammars.
A schematic representation of the paxtitioning
of a projection subgrammar into subgrammars is
2These are called
subgrammars
in Appeio, Fellinger &
Landsbergen(1987)
3Apart from these subgrammars there is also a projection
subgrammar to derive simple NPs, which is not partially
isomorphic to the other projection subgrammars.
-81 -
given in figure 1, where X is a variable over the
major syntactic categories. A projection subgram-
mar is a set of subgrammars that define a projec-
tion for a given category X. A projection of some
category X is a syntactic structure headed by X.
Each projection subgrammar is bifurcated as in-
dicated in figure 1. If the rules and transforma-
tions in the XPPtoGLAUSE and CLAUSEtoSEN-
TENCE subgrammars are applied a full clause is
derived. If the rules and transformations of the

XPPtoXPFORMULA (XPPtoXPF) and XPFOR-
MULAtoXPP (XPFtoXPP) are applied a 'small
clause' is derived.
The projection subgrammars are partially iso-
morphic to one another, which makes it possible
to translate a subset of constructions from one
projection subgrammar into constructions from
some other projection subgrammar. Furthermore
the XPPtoXPF subgrammars are partially isomor-
phic to the XPPtoCLAUSE subgrammars, and
the XPFtoXPP subgramlnars are partially isomor-
phic to the CLAUSEtoSENTENGE subgrammars.
This makes it possible to translate a subset of full
clauses into 'small clauses'.
The subgrammars are partially isomorphic to
one another instead of fully isomorphic, because
for certain full clauses no corresponding small
clauses exist (e.g. there is no 'small clause' cor-
responding to the full clause
Is he Jill).
BX
derivation
] XPP I
formation
I I
to ix Pf
CLAUSE I XPF
1 ,l
CLAUSE to XPF to
SENTENC~ XPP

Figure 1: The global organization of the Rosetta
projection subgrammars. X is a variable ranging
over the major syntactic categories
The subgrammars indicated in figure 1 will be
discussed in more detail now.
X-Derivation subgrammar deals with deriva-
tion and composition
XPPformation
In this subgrammar the
argu-
ment structure
and the syntactic realization
of arguments (whether they are subject, ob-
ject, prepositional object, etc.) is accounted
for. Voice (active, passive) is determined in
this subgrammar.
XPPtoCLAUSE
When this subgrammar is ap-
plied a full clause will be derived. In the
sub-
grammar
propositional complements and ad-
verbials are introduced, tense and aspect
is
determined and auxiliaries are introduced ac-
cordingly. There are several transformations
in this subgrammar to deal with the proper
incorporation of propositional units into the
structure, e.g. transformations dealing with
control phenomena, and transformations deal-

ing with the proper positioning of verbs (es-
pecially in Dutch). 'Hidden' arguments, e.g.
nonovert by-phrases in passives, are dealt with
here.
XPPtoXPF When this subgrammar is applied a
'small clause' will be derived. The XPPtoXPF
subgrammars are partially isomorphic to the
XPPtoCLAUSE subgrammars, hence they
contain similar corresponding rules. They
contain rules introducing propositional com-
plements, rules determining tense and aspect
(which is considered to be present though
dependent upon superordinate clauses) and
rules dealing with hidden arguments.
CLAUSEtoSENTENCE In this subgrammar
nonpropositional arguments are introduced
and scope of quantificational expressions is ac-
counted for. Furthermore the 'mood' of a sen-
tence is determined, i.e. it is decided whether
it is going to be a declarative, interrogative,
relative etc. clause.
XPFtoXPP
This subgrammar is partially iso-
morphic to the GLAUSEtoSENTENCE sub-
grammars. It contains rules to introduce non-
propositional arguments and to account for
scope. There are 'mood' rules determining
whether the XPP is 'closed' (i.e. there are no
free variables left in the structure), or 'open',
(i.e. the subject variable is free).

- 82 -
4 ILLUSTRATIONS
The global organization of the grammar will be
illustrated here by showing the derivation pro-
cesses of certain examples involving a categorial
mismatch and of some examples of translations
from 'small clauses' into full clauses or vice versa. I
repeat that only the generative part of the deriva-
tion need be demonstrated given the reversibility
of the grammars. Furthermore only the correct
derivation paths through the grammar will be il-
lustrated, though in reality many false paths, i.e.
paths through the grammar that do not lead to an
actual sentence, are chosen by the grammar.
Since M-grammaxs are reversible it possible to
'translate' from e.g. Dutch into Dutch. In this way
Rosetta functions as a paraphrase generator. Be-
cause of this, the partial isomorphy between two
projection subgrammars can (and will) be illus-
trated by showing the parallel derivation of two
paraphrases in generation.
In subsection 4.1 the derivation of hi] schaamt
zich ervoor and he is ashamed of it will be illus-
trated.
In subsection 4.2 the derivation of I find him
intelligent and I find that he is intelligent will be
illustrated.
In subsection 4.3 the derivation of he seems in-
telligent, he seems to be intelligent and it seems
that he is intelligent as paraphrases of one another

will be illustrated.
In subsection 4.4 the derivation of de op haar
verliefde man and de man die op haar verliefd is
as paraphrases of one another will be illustrated.
In subsection 4.5 the derivation of hi] zwemt
graag and he likes to swim will be illustrated.
4.1 Adjective-Verb
The derivations of hi] schaamt zich ervoor (lit. he
ashamed himself therefor) and
its translation
he is
ashamed of it run as follows. The verb schamen
is a two place verb so that it can be combined
with two variables, zl and ~, in the VPPforma-
tion subgrammar yielding VPP(xl x2 schaam}. In
the English grammar, the adjective ashamed is also
combined with two variables in the ADJPPfor-
mation subgrammar, yielding ADJPP(zi ashamed
z2}. The Dutch verb schamen must realize its sec-
ond argument as a prepositional object with the
preposition voor. The English adjective ashamed
must realize its second argument as a prepositional
object as well, though headed by the preposition of.
Pattern transformations axe applied to yield this
effect: VPP(zl
voor r¢ schaam}
and ADJPP(zi
ashamed of
z2).
Ill the VPPformation snbgrammar a Voice-rule

applies determining that the structure is in active
voice. In the ADJPPformation subgrammax a cor-
responding rule applies which has no visible effects.
In Dutch a transformation spelling out a reflex-
ive pronoun must apply, since the verb schamen
is a so-called inherently reflexive verb. This yields
VPP(zi zieh voor x2 schaam). Since spelling out
these reflexive pronouns is achieved by transfor-
mations, no corresponding M-rule need apply in
English.
These structures are both input to the XPPto-
CLAUSE subgrammar where they are turned into
clauses. In Dutch this yields CLAUSE(zi zieh soor
z2 schaam). In English the copula be is introduced,
yielding OLAUSE(zi be ashamed of x2}. Tense and
aspect rules are applied in both cases, putting the
structures in present tense, yielding OLAUSE(xi
zich voor x2 schaamt) and OLAUSE(zx is ashamed
of ~).
Substitution rules substitute the NPs her and
it respectively for the variables z2 and the NPs
hi] and he respectively for the variables zt. This
yields in English OLAUSE(he is ashamed of it) and
in Dutch OLAUSE(hij zich voor het schaamt). An
obligatory transformation turns voor het in Dutch
into ervoor.
Mood rules are applied in Dutch and in En-
glish. The clauses are turned into declarative main
clauses. In English this yields SENTENCE(he
is ashamed of it} and in Dutch this yields SEN-

TENCE(hij zich ervoor schaamt}. Application of
the transformation putting the finite verb in 'sec-
ond' position and application of an obligatory topi-
calization transformation in Dutch yield the actual
sentence Hij schaamt zich ervoor.
4.2 Adjective-declarative
with main verb
clause
The parallel derivations of I find him intelligent
and I find that he is intelligent run as follows.
In the ADJPPformation subgrammar the adjective
intelligent is combined with a variable zi yielding
ADJPP(zi intelligent) This ADJPP can be turned
either into a clause yielding OLAUSE(zi be intel-
ligent)
(ill tlle XPPtoOLAUSE subgrammax) or it
can continue as an adjectival construction (in the
ADJPPtoADJPF subgrammar). Tense and As-
pect rules determine that the tense of this con-
struction is dependent on the tense of a superor-
dinate construction yet to be formed. A substitu-
- 83 -
tion rule substitutes the NP containing
he
for
zl
yielding ADJPF{
he intelligent)
and CLAUSE{he
is/was intelligent}

respectively. Finally Mood rules
determine the way the clause and the ADJPF
are realized. The mood rule forming subordi-
nate declarative clauses is mapped onto the mood
rule forming 'closed' ADJPPs (CADJPP). Apply-
ing these mood rules yields
SENTENCE{that he
is/was intelligent)
and CADJPP(he
intelligent).
These results can be used later in the derivation
as arguments to the verb
.find.
To derive the rest of the structures the verb
find
is combined with two variables (z2, x3 ) yield-
ing VPP{x2 find z3). The substructures built
earlier can be substituted for x3 yielding VPP(
x2 find he intelligent)
and VPP(zz
find that he
is/was intelligent)
respectively. After turning
these VPPs into clauses and applying tense and as-
pect rules (putting the sentences ill present tense)
the tense of the subordinate clause can be deter-
mined. This yields CLAUSE(z2
find he intelligent}
and CLAUSE(z2
find that he is intelligent). Ap-

plying a case-assignment transformation and sub-
stituting the NP(I) for ~ yields CLAUSE(/find
him intelligent}
and CLAUSE{/find
that he is in-
telligent}
respectively. Applying a mood rule that
turns these clauses into declarative main clauses
yields the actual sentences.
4.3 Adjective-declarative clause
with copula
The derivations of
he seems intelligent, he seems
to be intelligent
and
it seems that he is intelli-
gent
starts in the same way as in the preceding
section. A CADJPP(he
intelligent)
and a SEN-
TENCE(that he is/was intelligent}
are generated.
In addition to the mood rule forming finite declar-
ative subordinate sentences a nmod rule forming
'closed' infinite declarative subordinate sentences
containing
to
call be applied. This rule forms
the SENTENCE(he

to be intelligent)
out of the
CLAUSE(he
be intelligent ).
These results can be used as arguments to tile
verb
seem.
In the VPPformation subgrammar a
VPP(seem
z2) is formed from the verb
seem
and
the variable z2. The SENTENCEs and the CAD-
JPP obtained earlier are substituted for the vari-
able x2. This yields the structures
VPP(seem he
intelligent}, VPP(seem that he is/was intelligent}
and
VPP(seem he to be intelligent}
respectively.
A transformation turns the subject of embedded
infinitival complements of verbs such as
seem
into
the subject of
seem,
and the NP(it} is inserted as
a subject of the verb
seem
if it has a finite com-

plement. After determining tense and aspect and
applying a subject-verb agreement transformation
this yields the structures CLAUSE(he
seems in-
telligent),
CLAUSE(it
seems that he is intelligent)
and CLAUSE(he
seems to be intelligent}
respec-
tively. Applying the mood rule forming declarative
main clauses yields the actual sentences.
In tile grammar of Dutch parallel derivations can
be made. The CADJPP(hff
intelligent)
(cf.
he in-
telligent}
and tile SENTENCEs
dat hij intelligent
is/was
and
hi3" intelligent te zijn
(cf.
that he is/was
intelligent
and
he to be intelligent
resp.) can be de-
rived.

Some of these results can be used as arguments
to the verb
sehijnen 'seem'.
In the VPPforma-
lion subgrammar the verb
sehijnen
is combined
with the variable z¢ into a VPP(z~
sehijn).
The
SENTENCEs obtained earlier can be substituted
for this variable, but tile CADJPP(h/j
intelligent)
cannot, because the Dutch verb
sehijnen
does not
take CADJPPs as a complement.
Tile derivation continues with the two results
VPP( dat hij is~was intelligent schffn)
and VPP(h/j
intelligent te zijn schijn}.
Application of several
transformations to deal adequately with such com-
plements in Dutch (Verb-raising and extraposition
(in tile sense of Evers(1975)), subject-to-subject-
raising and some others) and application of tense
and aspect rules yields
CLAUSE(her schijnt dat hij
intelligent is)
and

CLAUSE{hij intelligent sehijnt
te zijn)
respectively.
Application of mood rules forming declarative
main clauses and some obligatory transformations
in Dutch yields tile actual sentences
Het sehijnt
dat hij intelligent is
and
Hi] sehijnt intelligent te
zijn
as translations of tile English sentences derived
earlier.
4.4
Adjective-relative clause
The derivations of
(de) op haar verliefde (man)
(the man in love with her) and (de man) die op
haar verliefd is (the man that is in love with her)
runs as follows.
The adjective
verliefd 'in love'
is a two-place
adjective that is combined with two variables xl
and x¢ in tile ADJPPformation subgrammar. This
yields a structure of the form ADJPP(xl
verlie[d
~). The adjective
verliefd
must realize its second

argument (z2) as a prepositional object that can
occur in front of the adjective. Pattern transfor-
mations introduce the preposition required, yield-
ing ADJPP(sl
op z~ verliefd ).
- 84 -
This ADJPP can be turned into a clause, or it
can be turned into an adjectival phrase. The XP-
PROPtoGLAUSE subgrammar changes the struc-
ture mentioned in the following way: OLAUSE(zl
op z2 verliefd zi3"n),
where the top category has
been turned into CLAUSE and tile copula
zi3"n 'be'
has been introduced. To form all adjectival phrase
the ADJPP is input to the XPPtoXPF subgram-
mar, yielding ADJPF(zl op ~ verliefd). In both
subgrammars tense and aspect rules apply.
In the CLAUSEtoSENTENCE subgrammar a
transformation is applicable that moves the sub-
ject variable zl into a position where normally rel-
ative pronouns would appear. In this particular
structure this has no effects on the hft-right order,
but the relation that zl bears is changed.
In the CLAUSEtoSENTENGE subgramlnar and
in the ADJPFtoADJPP subgrammar the NP(zij)
'she' is substituted for variable ~ and the appro-
priate Case form (accusative) is assigned to it.
This yields CLAUSE(z~ op haar verliefd is/was)
and ADJPP(zi op haar verliefd).

Finally Mood rules turn tlle ADJPP into an
'open' ADJPP (OADJPP} yielding OADJPP(zl
op haar verliefd}, and they turn the CLAUSE into
a relative subordinate clause: SENTENGE(zl op
haar verliefd is). These structures can be used by
rules in the NP-subgrammar that introduce these
structures as modifiers and bind variable zl.
4.5 Graag-like
In the Dutch sentence hij zwemt graag the adverb
graa9 appears. This adverb must be mapped onto
the English verb like in the translation he likes to
swim.
It is assumed that the Dutch adverb graa9 is a
two place-function. This is required in Rosetta, be-
cause its translation like is a two-place function 4.
However, apart from being required in Rosetta, it
is also plausible for independent reasons that 9raa9
is a two-place function: the adverb 9raag imposes
selectional restrictions upon the subject of the sen-
tence it appears in (cf. fhet regent 9raag or fde
steen valt graag, which are as odd as their English
counterparts fit likes to rain and fThe stone likes
to
fall). If we assume that predicates impose sehc-
tional restrictions only upon their arguments, then
it must be the case that the subject of the sentence
is an argument of 9raag, or that the argument of
4This contrasts with the approach in the Eurotra frame-
work, where this requirement does not hold. See Arnold et.
aL (19as)

9raag is coindexed with the subject of tile sentence.
I will assmne tlle latter.
Starting with the subordinate infinitival clause
in English, we combine the verb swim, which takes
one argument, with a variable zl as its subject,
yielding: VPP(zl swim) Similarly in the Dutch
grammar the translation of swim, zwem, is com-
bined with zl: VPP(zl zwem) Ill tile VPPfor-
mation subgrammar the voice rule to form active
clauses is applied.
After tile VPPformation subgrammar the
derivation continues in tile XPPtoGLAUSE sub-
grammar. All M-ruh to make the sentence infini-
tival is applied. Corresponding rules are applied in
the XPPtoCLAUSE subgrammar
of
Dutch.
In the GLAUSEtoSENTENCE subgrammar no
arguments are substituted. In English a rule is ap-
plied that makes the clause all infinitival subordi-
nate clause containing
to
and containing a free vari-
able in subject position which will later be subject
to control transformations. This yields a structure
of the form SENTENGE(zl
to swim)
In Dutch a corresponding rule is applied that
makes the clause all infinitival subordinate clause
without

te
with a free variable in subject posi-
tion. This yields the following structure in Dutch:
SENTENCE(zx
zwemmen)
These structures will
be used later on.
In the VPPformation subgrammar of English
the two-place verb
like
is combined with two vari-
ables,
zl and x2. This yields: VPP(zi like x2) The
voice rule to form active sentences is applied.
Correspondingly, in the ADVPPformation sub-
grammar of Dutch tile adverb 9raa9 is combined
with two variables, zl and za, and a voice rules is
applied. This yields: ADVPP(zl 9raa9 z2}
In the English subgrammar XPPtoCLAUSE tile
sentential structure derived above is substituted
for the variable x~, yielding: VPP(zi like [ xl to
swim]}
A
control transformation deletes the second oc-
currence of zl. Tense and aspect rules apply which
turn the structure into a finite clause in present
tense.
In the Dutch
subgrammar
XPPtoCLAUSE the

sentential structure derived above is substituted
for the variable z¢ by a special rule that takes care
of substitution of sentential complements into AD-
VPPs. This special rule deletes the ADVPP node
and replaces it by a VPP node, turns the ADVP
into a modifier inside this VPP, makes the VP of
SENT the VP of this VPP, deletes the variable zl
inside SENT and un-does the morphological effects
of tense rules. This yields the structure: VPP(zl
- 85 -
AD VP(graag} zwem)
These structures continue their normal deriva-
tion. Tense and aspect rules apply, the NP ar-
gument
hij" (he)
is substituted for st and the sen-
tence is made into a declarative main clause, yield-
ing in English: SENTENCE(he
likes to swim)
and
in Dutch, after application of the transformation
of 'Verb second' and an obligatory topicalization
transformation:
SENTENCE( hij zwemt graag)
5 CONCLUSION
It has been shown that the concept of partial iso-
morphy between subgrammars makes it possible to
translate between words of different syntactic cat-
egories and between 'small clauses' and full clauses
in a systematic way. Furthermore, it has been

shown that one of the most difficult cases of trans-
lation between words of different categories, viz.
the
9raa9/like
translation probhm, can be reduced
to having only one special rule, given partial iso-
morphy between subgrammars.
ACKN O WLED GEMENT S
This paper is based on joint work being done in the
Rosetta machine translation project. I would like
to thank Lisette Appelo, Jan Landsbergen, Mar-
greet Sanders and Andr6 Schenk for many valuable
comments on earlier drafts of this paper.
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